Centroid Molecular Dynamics Can Be Greatly Accelerated Through Neural Network Learned Centroid Forces Derived from Path Integral Molecular Dynamics

TL;DR

This paper introduces ML-CMD, a neural network-based method that accelerates centroid molecular dynamics by learning effective forces from path integral data, achieving similar accuracy with less computational effort.

Contribution

The paper presents a novel neural network approach to efficiently approximate centroid forces, significantly reducing computational costs in quantum dynamics simulations.

Findings

ML-CMD achieves comparable accuracy to traditional methods.

The approach reduces computational cost substantially.

Validated on liquid para-hydrogen and water systems.

Abstract

For nearly the past 30 years, Centroid Molecular Dynamics (CMD) has proven to be a viable classical-like phase space formulation for the calculation of quantum dynamical properties. However, calculation of the centroid effective force remains a significant computational cost and limits the ability of CMD to be an efficient approach to study condensed phase quantum dynamics. In this paper we introduce a neural network-based methodology for first learning the centroid effective force from path integral molecular dynamics data, which is subsequently used as an effective force field to evolve the centroids directly with the CMD algorithm. This method, called Machine-Learned Centroid Molecular Dynamics (ML-CMD) is faster and far less costly than both standard on the fly CMD and ring polymer molecular dynamics (RPMD). The training aspect of ML-CMD is also straightforwardly implemented utilizing the DeepMD software kit. ML-CMD is then applied to two model systems to illustrate the approach: liquid para-hydrogen and water. The results show comparable accuracy to both CMD and RPMD in the estimation of quantum dynamical properties, including the self-diffusion constant and velocity time correlation function, but for significantly reduced overall computational cost.